- Some maintenance fixes

- Start of the examples vignette



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+% $Id: examples.Rnw 66 2010-09-03 08:50:26Z jranke $
+%%\VignetteIndexEntry{Examples for kinetic evaluations using mkin}
+%%VignetteDepends{FME}
+%%\usepackage{Sweave}
+\documentclass[12pt,a4paper]{article}
+\usepackage{a4wide}
+%%\usepackage[lists,heads]{endfloat}
+\input{header}
+\hypersetup{  
+  pdftitle = {Examples for kinetic evaluations using mkin},
+  pdfsubject = {Manuscript},
+  pdfauthor = {Johannes Ranke},
+  colorlinks = {true},
+  linkcolor = {blue},
+  citecolor = {blue},
+  urlcolor = {red},
+  hyperindex = {true},
+  linktocpage = {true},
+}
+
+\begin{document}
+\title{Examples for kinetic evaluations using mkin}
+\author{\textbf{Johannes Ranke} \\[0.5cm]
+%EndAName
+Eurofins Regulatory AG\\
+Weidenweg 15, CH--4310 Rheinfelden, Switzerland\\[0.5cm]
+and\\[0.5cm]
+University of Bremen\\
+}
+\maketitle
+
+%\begin{abstract}
+%\end{abstract}
+
+
+\thispagestyle{empty} \setcounter{page}{0}
+
+\clearpage
+
+\tableofcontents
+
+\textbf{Key words}: Kinetics, FOCUS, nonlinear optimisation
+
+\section{Kinetic evaluations for parent compounds}
+\label{intro}
+
+These examples are also evaluated in a parallel vignette of the
+\Rpackage{kinfit} package \citep{pkg:kinfit}. The datasets are from Appendix 3,
+of the FOCUS kinetics report \citep{FOCUS2006, FOCUSkinetics2011}.
+
+\subsection{Laboratory Data L1}
+
+The following code defines example dataset L1 from the FOCUS kinetics
+report, p. 284
+
+\begin{Schunk}
+\begin{Sinput}
+R> library("mkin")
+R> FOCUS_2006_L1 = data.frame(
++   t = rep(c(0, 1, 2, 3, 5, 7, 14, 21, 30), each = 2),
++   parent = c(88.3, 91.4, 85.6, 84.5, 78.9, 77.6, 
++              72.0, 71.9, 50.3, 59.4, 47.0, 45.1,
++              27.7, 27.3, 10.0, 10.4, 2.9, 4.0))
+R> FOCUS_2006_L1_mkin <- mkin_wide_to_long(FOCUS_2006_L1)
+\end{Sinput}
+\end{Schunk}
+
+The next step is to set up the models used for the kinetic analysis. Note that
+the model definitions contain the names of the observed variables in the data.
+In this case, there is only one variable called \Robject{parent}.
+
+\begin{Schunk}
+\begin{Sinput}
+R> SFO <- mkinmod(parent = list(type = "SFO"))
+R> FOMC <- mkinmod(parent = list(type = "FOMC"))
+R> DFOP <- mkinmod(parent = list(type = "DFOP"))
+\end{Sinput}
+\end{Schunk}
+
+The three models cover the first assumption of simple first order (SFO),
+the case of declining rate constant over time (FOMC) and the case of two
+different phases of the kinetics (DFOP). For a more detailed discussion
+of the models, please see the FOCUS kinetics report.
+
+The following two lines fit the model and produce the summary report
+of the model fit. This covers the numerical analysis given in the 
+FOCUS report.
+
+\begin{Schunk}
+\begin{Sinput}
+R> m.L1.SFO <- mkinfit(SFO, FOCUS_2006_L1_mkin, quiet=TRUE)
+R> summary(m.L1.SFO)
+\end{Sinput}
+\begin{Soutput}
+mkin version:    0.9.10 
+R version:       2.15.2 
+Date of fit:     Sat Feb 16 21:38:15 2013 
+Date of summary: Sat Feb 16 21:38:15 2013 
+
+Equations:
+[1] d_parent = - k_parent_sink * parent
+
+Starting values for optimised parameters:
+              initial   type transformed
+parent_0        100.0  state  100.000000
+k_parent_sink     0.1 deparm   -2.302585
+
+Fixed parameter values:
+None
+
+Optimised, transformed parameters:
+              Estimate Std. Error
+parent_0        92.471      1.368
+k_parent_sink   -2.347      0.041
+
+Backtransformed parameters:
+              Estimate
+parent_0        92.471
+k_parent_sink    0.096
+
+Residual standard error: 2.948 on 16 degrees of freedom
+
+Chi2 error levels in percent:
+         err.min n.optim df
+All data   3.424       2  7
+parent     3.424       2  7
+
+Estimated disappearance times:
+        DT50  DT90
+parent 7.249 24.08
+
+Estimated formation fractions:
+            ff
+parent_sink  1
+
+Parameter correlation:
+              parent_0 k_parent_sink
+parent_0        1.0000        0.6248
+k_parent_sink   0.6248        1.0000
+
+Data:
+ time variable observed predicted residual
+    0   parent     88.3    92.471  -4.1710
+    0   parent     91.4    92.471  -1.0710
+    1   parent     85.6    84.039   1.5610
+    1   parent     84.5    84.039   0.4610
+    2   parent     78.9    76.376   2.5241
+    2   parent     77.6    76.376   1.2241
+    3   parent     72.0    69.412   2.5884
+    3   parent     71.9    69.412   2.4884
+    5   parent     50.3    57.330  -7.0301
+    5   parent     59.4    57.330   2.0699
+    7   parent     47.0    47.352  -0.3515
+    7   parent     45.1    47.352  -2.2515
+   14   parent     27.7    24.247   3.4527
+   14   parent     27.3    24.247   3.0527
+   21   parent     10.0    12.416  -2.4163
+   21   parent     10.4    12.416  -2.0163
+   30   parent      2.9     5.251  -2.3513
+   30   parent      4.0     5.251  -1.2513
+\end{Soutput}
+\end{Schunk}
+
+A plot of the fit is obtained with the plot function for mkinfit objects.
+
+\begin{Schunk}
+\begin{Sinput}
+R> plot(m.L1.SFO)
+\end{Sinput}
+\end{Schunk}
+\includegraphics{examples-L1_SFO_plot}
+
+The residual plot can be obtained using the information contained in the
+mkinfit object, which is in fact a derivative of an modFit object defined by
+the \Rpackage{FME} package.
+
+\begin{Schunk}
+\begin{Sinput}
+R> plot(m.L1.SFO$data$time, m.L1.SFO$data$residual,
++   xlab = "Time", ylab = "Residual", ylim = c(-8, 8))
+R> abline(h = 0, lty = 2)
+\end{Sinput}
+\end{Schunk}
+\includegraphics{examples-L1_SFO_residuals}
+
+For comparison, the FOMC model is fitted as well, and the $\chi^2$ error level
+is checked.
+
+\begin{Schunk}
+\begin{Sinput}
+R> m.L1.FOMC <- mkinfit(FOMC, FOCUS_2006_L1_mkin, quiet=TRUE)
+R> s.m.L1.FOMC <- summary(m.L1.FOMC)
+R> s.m.L1.FOMC$errmin
+\end{Sinput}
+\begin{Soutput}
+            err.min n.optim df
+All data 0.03618911       3  6
+parent   0.03618911       3  6
+\end{Soutput}
+\end{Schunk}
+
+Due to the higher number of parameters, and the lower number of degrees of freedom
+of the fit, the $\chi^2$ error level is actually higher for the FOMC model (3.6\%) than 
+for the SFO model (3.4\%).
+
+\subsection{Laboratory Data L2}
+
+The following code defines example dataset L2 from the FOCUS kinetics
+report, p. 287
+
+\begin{Schunk}
+\begin{Sinput}
+R> library("mkin")
+R> FOCUS_2006_L2 = data.frame(
++   t = rep(c(0, 1, 3, 7, 14, 28), each = 2),
++   parent = c(96.1, 91.8, 41.4, 38.7,
++              19.3, 22.3, 4.6, 4.6,
++              2.6, 1.2, 0.3, 0.6))
+R> FOCUS_2006_L2_mkin <- mkin_wide_to_long(FOCUS_2006_L2)
+\end{Sinput}
+\end{Schunk}
+
+Again, the SFO model is fitted and a summary is obtained.
+
+\begin{Schunk}
+\begin{Sinput}
+R> m.L2.SFO <- mkinfit(SFO, FOCUS_2006_L2_mkin, quiet=TRUE)
+R> summary(m.L2.SFO)
+\end{Sinput}
+\begin{Soutput}
+mkin version:    0.9.10 
+R version:       2.15.2 
+Date of fit:     Sat Feb 16 21:38:15 2013 
+Date of summary: Sat Feb 16 21:38:15 2013 
+
+Equations:
+[1] d_parent = - k_parent_sink * parent
+
+Starting values for optimised parameters:
+              initial   type transformed
+parent_0        100.0  state  100.000000
+k_parent_sink     0.1 deparm   -2.302585
+
+Fixed parameter values:
+None
+
+Optimised, transformed parameters:
+              Estimate Std. Error
+parent_0       91.4656      3.807
+k_parent_sink  -0.4112      0.107
+
+Backtransformed parameters:
+              Estimate
+parent_0        91.466
+k_parent_sink    0.663
+
+Residual standard error: 5.51 on 10 degrees of freedom
+
+Chi2 error levels in percent:
+         err.min n.optim df
+All data   14.38       2  4
+parent     14.38       2  4
+
+Estimated disappearance times:
+        DT50  DT90
+parent 1.046 3.474
+
+Estimated formation fractions:
+            ff
+parent_sink  1
+
+Parameter correlation:
+              parent_0 k_parent_sink
+parent_0        1.0000        0.4295
+k_parent_sink   0.4295        1.0000
+
+Data:
+ time variable observed     predicted residual
+    0   parent     96.1 91.4656079103   4.6344
+    0   parent     91.8 91.4656079103   0.3344
+    1   parent     41.4 47.1395280371  -5.7395
+    1   parent     38.7 47.1395280371  -8.4395
+    3   parent     19.3 12.5210295280   6.7790
+    3   parent     22.3 12.5210295280   9.7790
+    7   parent      4.6  0.8833842647   3.7166
+    7   parent      4.6  0.8833842647   3.7166
+   14   parent      2.6  0.0085318162   2.5915
+   14   parent      1.2  0.0085318162   1.1915
+   28   parent      0.3  0.0000007958   0.3000
+   28   parent      0.6  0.0000007958   0.6000
+\end{Soutput}
+\end{Schunk}
+
+The $\chi^2$ error level of 14\% suggests that the model does not fit very well.
+This is also obvious from the plots of the fit and the residuals.
+
+\begin{Schunk}
+\begin{Sinput}
+R> plot(m.L2.SFO)
+\end{Sinput}
+\end{Schunk}
+\includegraphics{examples-L2_SFO_plot}
+
+In the FOCUS kinetics report, it is stated that there is no apparent systematic
+error observed from the residual plot up to the measured DT90 (approximately at
+day 5), and there is an underestimation beyond that point.
+
+\begin{Schunk}
+\begin{Sinput}
+R> plot(m.L2.SFO$data$time, m.L2.SFO$data$residual,
++   xlab = "Time", ylab = "Residual", ylim = c(-10, 10))
+R> abline(h = 0, lty = 2)
+\end{Sinput}
+\end{Schunk}
+\includegraphics{examples-L2_SFO_residuals}
+
+We may add that it is difficult to judge the random nature of the residuals just 
+from the three samplings at days 0, 1 and 3. Also, it is not clear why a
+consistent underestimation after the approximate DT90 should be irrelevant.
+
+For comparison, the FOMC model is fitted as well, and the $\chi^2$ error level
+is checked.
+
+\begin{Schunk}
+\begin{Sinput}
+R> m.L2.FOMC <- mkinfit(FOMC, FOCUS_2006_L2_mkin, quiet=TRUE)
+R> plot(m.L2.FOMC)
+R> s.m.L2.FOMC <- summary(m.L2.FOMC)
+R> s.m.L2.FOMC$errmin
+\end{Sinput}
+\begin{Soutput}
+            err.min n.optim df
+All data 0.06204245       3  3
+parent   0.06204245       3  3
+\end{Soutput}
+\end{Schunk}
+\includegraphics{examples-L2_FOMC}
+
+The error level at which the $\chi^2$ test passes is much lower in this case.
+Therefore, the FOMC model provides a better description of the data, as less
+experimental error has to be assumed in order to explain the data.
+
+Fitting the four parameter DFOP model does not further reduce the 
+$\chi^2$ error level. 
+
+\begin{Schunk}
+\begin{Sinput}
+R> m.L2.DFOP <- mkinfit(DFOP, FOCUS_2006_L2_mkin, quiet=TRUE)
+R> plot(m.L2.DFOP)
+\end{Sinput}
+\end{Schunk}
+\includegraphics{examples-L2_DFOP}
+
+Here, the default starting parameters for the DFOP model obviously do not lead
+to a reasonable solution. Therefore the fit is repeated with different starting
+parameters.
+
+\begin{Schunk}
+\begin{Sinput}
+R> m.L2.DFOP <- mkinfit(DFOP, FOCUS_2006_L2_mkin, 
++   parms.ini = c(k1 = 1, k2 = 0.01, g = 0.8),
++   quiet=TRUE)
+R> plot(m.L2.DFOP)
+R> summary(m.L2.DFOP)
+\end{Sinput}
+\begin{Soutput}
+mkin version:    0.9.10 
+R version:       2.15.2 
+Date of fit:     Sat Feb 16 21:38:16 2013 
+Date of summary: Sat Feb 16 21:38:16 2013 
+
+Equations:
+[1] d_parent = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time))) * parent
+
+Starting values for optimised parameters:
+         initial   type transformed
+parent_0   1e+02  state 100.0000000
+k1         1e+00 deparm   0.0000000
+k2         1e-02 deparm  -4.6051702
+g          8e-01 deparm   0.9802581
+
+Fixed parameter values:
+None
+
+Optimised, transformed parameters:
+         Estimate Std. Error
+parent_0  93.9500         NA
+k1         4.9589         NA
+k2        -1.0880         NA
+g         -0.2821         NA
+
+Backtransformed parameters:
+         Estimate
+parent_0   93.950
+k1        142.434
+k2          0.337
+g           0.402
+
+Residual standard error: 1.732 on 8 degrees of freedom
+
+Chi2 error levels in percent:
+         err.min n.optim df
+All data   2.529       4  2
+parent     2.529       4  2
+
+Estimated disappearance times:
+       DT50 DT90
+parent   NA   NA
+
+Estimated formation fractions:
+[1] ff
+<0 rows> (or 0-length row.names)
+
+Data:
+ time variable observed predicted residual
+    0   parent     96.1 93.950000   2.1500
+    0   parent     91.8 93.950000  -2.1500
+    1   parent     41.4 40.143423   1.2566
+    1   parent     38.7 40.143423  -1.4434
+    3   parent     19.3 20.464500  -1.1645
+    3   parent     22.3 20.464500   1.8355
+    7   parent      4.6  5.318322  -0.7183
+    7   parent      4.6  5.318322  -0.7183
+   14   parent      2.6  0.503070   2.0969
+   14   parent      1.2  0.503070   0.6969
+   28   parent      0.3  0.004501   0.2955
+   28   parent      0.6  0.004501   0.5955
+\end{Soutput}
+\begin{Sinput}
+R> s.m.L2.DFOP <- summary(m.L2.DFOP)
+R> s.m.L2.DFOP$errmin
+\end{Sinput}
+\begin{Soutput}
+            err.min n.optim df
+All data 0.02528763       4  2
+parent   0.02528763       4  2
+\end{Soutput}
+\end{Schunk}
+\includegraphics{examples-L2_DFOP_2}
+
+Therefore, the FOMC model is clearly the best-fit model based on the 
+$\chi^2$ error level criterion.
+
+\subsection{Laboratory Data L3}
+
+The following code defines example dataset L3 from the FOCUS kinetics
+report, p. 290
+
+\begin{Schunk}
+\begin{Sinput}
+R> library("mkin")
+R> FOCUS_2006_L3 = data.frame(
++   t = c(0, 3, 7, 14, 30, 60, 91, 120),
++   parent = c(97.8, 60, 51, 43, 35, 22, 15, 12))
+R> FOCUS_2006_L3_mkin <- mkin_wide_to_long(FOCUS_2006_L3)
+\end{Sinput}
+\end{Schunk}
+
+SFO model, summary and plot:
+
+\begin{Schunk}
+\begin{Sinput}
+R> m.L3.SFO <- mkinfit(SFO, FOCUS_2006_L3_mkin, quiet=TRUE)
+R> summary(m.L3.SFO)
+\end{Sinput}
+\begin{Soutput}
+mkin version:    0.9.10 
+R version:       2.15.2 
+Date of fit:     Sat Feb 16 21:38:16 2013 
+Date of summary: Sat Feb 16 21:38:16 2013 
+
+Equations:
+[1] d_parent = - k_parent_sink * parent
+
+Starting values for optimised parameters:
+              initial   type transformed
+parent_0        100.0  state  100.000000
+k_parent_sink     0.1 deparm   -2.302585
+
+Fixed parameter values:
+None
+
+Optimised, transformed parameters:
+              Estimate Std. Error
+parent_0        74.873      8.458
+k_parent_sink   -3.678      0.326
+
+Backtransformed parameters:
+              Estimate
+parent_0        74.873
+k_parent_sink    0.025
+
+Residual standard error: 12.91 on 6 degrees of freedom
+
+Chi2 error levels in percent:
+         err.min n.optim df
+All data   21.24       2  6
+parent     21.24       2  6
+
+Estimated disappearance times:
+        DT50  DT90
+parent 27.43 91.12
+
+Estimated formation fractions:
+            ff
+parent_sink  1
+
+Parameter correlation:
+              parent_0 k_parent_sink
+parent_0        1.0000        0.5484
+k_parent_sink   0.5484        1.0000
+
+Data:
+ time variable observed predicted  residual
+    0   parent     97.8    74.873  22.92734
+    3   parent     60.0    69.407  -9.40654
+    7   parent     51.0    62.734 -11.73403
+   14   parent     43.0    52.563  -9.56336
+   30   parent     35.0    35.083  -0.08281
+   60   parent     22.0    16.439   5.56137
+   91   parent     15.0     7.510   7.48961
+  120   parent     12.0     3.609   8.39083
+\end{Soutput}
+\begin{Sinput}
+R> plot(m.L3.SFO)
+\end{Sinput}
+\end{Schunk}
+\includegraphics{examples-L3_SFO}
+
+The $\chi^2$ error level of 22\% as well as the plot suggest that the model
+does not fit very well. 
+
+The FOMC model performs better:
+
+\begin{Schunk}
+\begin{Sinput}
+R> m.L3.FOMC <- mkinfit(FOMC, FOCUS_2006_L3_mkin, quiet=TRUE)
+R> plot(m.L3.FOMC)
+R> s.m.L3.FOMC <- summary(m.L3.FOMC)
+R> s.m.L3.FOMC$errmin
+\end{Sinput}
+\begin{Soutput}
+            err.min n.optim df
+All data 0.07321867       3  5
+parent   0.07321867       3  5
+\end{Soutput}
+\begin{Sinput}
+R> endpoints(m.L3.FOMC)
+\end{Sinput}
+\begin{Soutput}
+$distimes
+           DT50     DT90
+parent 7.729478 431.2428
+
+$ff
+logical(0)
+
+$SFORB
+logical(0)
+\end{Soutput}
+\end{Schunk}
+\includegraphics{examples-L3_FOMC}
+
+The error level at which the $\chi^2$ test passes is 7\% in this case.
+
+Fitting the four parameter DFOP model further reduces the $\chi^2$ error level
+considerably:
+
+\begin{Schunk}
+\begin{Sinput}
+R> m.L3.DFOP <- mkinfit(DFOP, FOCUS_2006_L3_mkin, quiet=TRUE)
+R> plot(m.L3.DFOP)
+R> s.m.L3.DFOP <- summary(m.L3.DFOP)
+R> s.m.L3.DFOP$errmin
+\end{Sinput}
+\begin{Soutput}
+            err.min n.optim df
+All data 0.02223992       4  4
+parent   0.02223992       4  4
+\end{Soutput}
+\end{Schunk}
+\includegraphics{examples-L3_DFOP}
+
+Therefore, the DFOP model is the best-fit model based on the $\chi^2$ error
+level criterion for laboratory data L3.
+
+\subsection{Laboratory Data L4}
+
+The following code defines example dataset L4 from the FOCUS kinetics
+report, p. 293
+
+\begin{Schunk}
+\begin{Sinput}
+R> library("mkin")
+R> FOCUS_2006_L4 = data.frame(
++   t = c(0, 3, 7, 14, 30, 60, 91, 120),
++   parent = c(96.6, 96.3, 94.3, 88.8, 74.9, 59.9, 53.5, 49.0))
+R> FOCUS_2006_L4_mkin <- mkin_wide_to_long(FOCUS_2006_L4)
+\end{Sinput}
+\end{Schunk}
+
+SFO model, summary and plot:
+
+\begin{Schunk}
+\begin{Sinput}
+R> m.L4.SFO <- mkinfit(SFO, FOCUS_2006_L4_mkin, quiet=TRUE)
+R> summary(m.L4.SFO)
+\end{Sinput}
+\begin{Soutput}
+mkin version:    0.9.10 
+R version:       2.15.2 
+Date of fit:     Sat Feb 16 21:38:17 2013 
+Date of summary: Sat Feb 16 21:38:17 2013 
+
+Equations:
+[1] d_parent = - k_parent_sink * parent
+
+Starting values for optimised parameters:
+              initial   type transformed
+parent_0        100.0  state  100.000000
+k_parent_sink     0.1 deparm   -2.302585
+
+Fixed parameter values:
+None
+
+Optimised, transformed parameters:
+              Estimate Std. Error
+parent_0         96.44      1.949
+k_parent_sink    -5.03      0.080
+
+Backtransformed parameters:
+              Estimate
+parent_0        96.442
+k_parent_sink    0.007
+
+Residual standard error: 3.651 on 6 degrees of freedom
+
+Chi2 error levels in percent:
+         err.min n.optim df
+All data   3.288       2  6
+parent     3.288       2  6
+
+Estimated disappearance times:
+       DT50 DT90
+parent  106  352
+
+Estimated formation fractions:
+            ff
+parent_sink  1
+
+Parameter correlation:
+              parent_0 k_parent_sink
+parent_0        1.0000        0.5865
+k_parent_sink   0.5865        1.0000
+
+Data:
+ time variable observed predicted residual
+    0   parent     96.6     96.44   0.1585
+    3   parent     96.3     94.57   1.7324
+    7   parent     94.3     92.13   2.1744
+   14   parent     88.8     88.00   0.7972
+   30   parent     74.9     79.26  -4.3589
+   60   parent     59.9     65.14  -5.2376
+   91   parent     53.5     53.18   0.3167
+  120   parent     49.0     43.99   5.0054
+\end{Soutput}
+\begin{Sinput}
+R> plot(m.L4.SFO)
+\end{Sinput}
+\end{Schunk}
+\includegraphics{examples-L4_SFO}
+
+The $\chi^2$ error level of 3.3\% as well as the plot suggest that the model
+fits very well. 
+
+The FOMC model for comparison
+
+\begin{Schunk}
+\begin{Sinput}
+R> m.L4.FOMC <- mkinfit(FOMC, FOCUS_2006_L4_mkin, quiet=TRUE)
+R> plot(m.L4.FOMC)
+R> s.m.L4.FOMC <- summary(m.L4.FOMC)
+R> s.m.L4.FOMC$errmin
+\end{Sinput}
+\begin{Soutput}
+            err.min n.optim df
+All data 0.02027643       3  5
+parent   0.02027643       3  5
+\end{Soutput}
+\end{Schunk}
+\includegraphics{examples-L4_FOMC}
+
+The error level at which the $\chi^2$ test passes is slightly lower for the FOMC 
+model. However, the difference appears negligible.
+
+\bibliographystyle{plainnat}
+\bibliography{references}
+
+\end{document}
+% vim: set foldmethod=syntax: